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Chapter 4: Q 4.34 (page 394)

Translate to a system of equations and then solve:

The difference of two complementary angles is 80degrees. Find the measures of the angles.

Short Answer

Expert verified

The measure of angles are85鈭� and 5鈭�.

Step by step solution

01

Step 1. Given

We are given that the difference between two complementary angles is 80鈭�.

02

Step 2. Formation of equations

We know that the sum of complementary angles is equal to 90鈭�.

Let the one angle be x, and the other angle will be y, so the equation will be,

localid="1644600128864" x+y=90鈭�y=90鈭�-x,

The difference between the angles is 80鈭�, so the equation will be,

x-y=80鈭�x-(90鈭�-x)=80鈭�

03

Step 3. Solving the equation.

Solving x-(90鈭�-x)=80鈭�

x-90鈭�+x=80鈭�2x-90鈭�=80鈭�2x=80鈭�+90鈭�2x=170鈭�

Dividing by 2, we get

x=85鈭�

And the other angle will be90鈭�-85鈭�=5鈭�.

04

Step 4. Checking the solution  

Checking the solution by putting the value of x,yin the equations, we get

x+y=90鈭�85鈭�+5鈭�=90鈭�90鈭�=90鈭�x-y=80鈭�85鈭�-5鈭�=80鈭�80鈭�=80鈭�

This is true, hence the solution is correct.

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